Merging History Trees of Dark Matter Haloes: a Tool for Exploring Galaxy Formation Models

A method of deriving and using merging history trees of dark matter galaxy haloes directly from pure gravity N-body simulations is presented. This combines the full non-linearity of N-body simulations with the flexibility of the semi-analytical approach. Merging history trees derived from power-law initial perturbation spectrum simulations (for indices n=-2 and 0) by Warren et al. are shown. As an example of a galaxy formation model, these are combined with evolutionary stellar population synthesis, via simple scaling laws for star formation rates, showing that if most star formation occurs during merger-induced bursts, then a nearly flat faint-end slope of the galaxy luminosity function may be obtained in certain cases. Interesting properties of hierarchical halo formation are noted as follows. (1) In a given model, merger rates may vary widely between individual haloes, and typically ~20-30 per cent of a halo's mass may be a result of the infall of uncollapsed material. (2) Small-mass haloes continue to form at recent times: as expected, the existence of young, low-redshift, low-metallicity galaxies is consistent with hierarchical galaxy formation models. (3) For n=-2, the halo spatial correlation function can have a very high initial bias owing to the high power on large scales.